Description: This proposed MERIT extension is a logical continuation of the current award, revolving around the development of new statistical methods and their application to studies involving cancer and nutrition. The following broad topics will be considered. Analysis of Dietary Intake Data: In conjunction with researchers at the NCI, we have developed access to a number of exciting dietary intake data sets, including a major biomarker study, two major surveillance studies and a major prospective cohort study. Our NCI-Method for estimating the usual intake of foods uses one food at a time: we will get greater efficiency by developing methods for multiple foods simultaneously. Also, issues such as the healthy eating index (HEI) motivate the need to model multiple food intakes and nutrients simultaneously: we will develop those models and also statistical methods to fit them. Diet and Colon Carcinogenesis: We will develop semiparametric statistical methods for hierar- chical functional data to analyze a series of studies, done at the cellular level, involving diet, apoptosis, cellular response and colon carcinogenesis. Our new approach, based on a novel formulation of func- tional principal components, allows understanding of the effects of cell position in the colonic crypts, as well as incorporating crypt signahng, i.e., correlations of response among the crypts themselves. Semiparametric Methods: We will develop a series of novel statistical methods motivated by issues of gene-environment interaction studies. First, in case-control studies, we have shown that great gains in efficiency can be made if one can assume that genetic and environmental factors are independent in the population, possibly after conditioning on factors to account for population strat- ification. We will develop novel shrinkage approaches that allow efficient gene-environment inference with independence given strata holds but that are robust to deviations from this assumption. Second, we will consider studies for which the main interest is in whether there are genetic effects, but there is the possibility for gene-environment interaction. We will develop novel score-type tests for genetic effects in this context, where the careful use of projection ensures efficient inference. In the case of many genes, or SNPs, we will again use shrinkage ideas to improve the performance of score-type testing. This work will be extended to additive models and repeated measures/longitudinal data.